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0^n

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Wiht
n
a real number, we have
     
0n =
  
 if n   <   0,
1  if n   =   0,
0  if n   >   0.

Note that for 0 0 we have the empty product, i.e. 1.

A000007 The characteristic function of 0:
a (n) = 0n, n   ≥   0
.
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}

See also